-
Notifications
You must be signed in to change notification settings - Fork 7
Multi Stage Adaptive Trial Design in R
Optimizing the clinical trial design is essential to decrease the cost of drug development as a typical clinical trial usually costs millions of U.S. dollars. In designing the trials, we need to balance the statistical power and the total cost, which are conflicting. This becomes more complicated in the setup of personalized medicine and adaptive trial design where there are multiple subpopulations and multiple states for decision making. Recently, [1] provides a general approach to formulate multi-stage decision-making problems with Bayes risk constraints as sparse LP problems. As a specific application, [1] formulates the two-stage and two-subpopulation adaptive trial design problem as a sparse linear programming (LP) problem, and solves this problem by commercial solvers such as Gurobi. The resulting designs substantially improve existing benchmarks. In practice, it is of interest to consider cases where there are more than two subpopulations or two stages. However, having one more subpopulation or one more stage will increase the problem size exponentially, and make the current approach computationally infeasible.
This project aims to develop new customized algorithms and R package for this problem with three key features: 1) It provides a highly efficient solver to tackle a large and important class of LP problems; 2) It provides a solution for multi-stage decision-making problems with Bayes risk constraints; 3) It provides additional functions such as visualizing the optimal decision maps.
Solving LP problems is of central importance in operations research, statistics and computer sciences. There are mainly two classes of practical algorithms for solving LP problems, interior-point algorithms [2] and simplex algorithms. Interior-point algorithms achieve polynomial-time complexities. However, the complexity increases at a cubic rate with respect to the problem size, and does not scale with our problem size, which can be of dimension millions by millions. In comparison, simplex methods work well in practice, though its worst-case complexity grows exponentially.
Both these two classes of algorithms are designed for general LP problems, which do not fully take our specific problem structures into consideration. Our class of LP problems is highly sparse and highly structured. We propose to solve the nonsmooth dual problem and exploit dual sparsity of the LP problem. Our preliminary results show that this approach substantially improves the computational efficiency, and achieves the solvability for more sophisticated problems that were previously regarded as unsolvable.
We aim to develop an efficient R package for a large class of LP-based adaptive trial design problems, or, more broadly, multi-stage decision-making problems. The package has two key components: a customized optimization engine and a user-friendly interface for multi-stage decision-making problems. The optimization engine will be written in C++ that solves our class of LP problems efficiently. This engine will be optimized for our particular class of LP problems. In particular, in solving the nonsmooth dual problem, we will develop a specialized algorithm framework with iterative subspace optimization and row generation phases that is particularly efficient for our problems. Meanwhile, we will implement the user interface for adaptive trial design problems, where the user could specify his/her requirement and objective. In addition, we will provide a visualization function for visualizing the optimal decision map.
The delivered R packages will provide an efficient tool that can solve a wide class of adaptive trial design problems and decision-making problems with Bayes risk constraints. It will be the first R package that solves this broad class of problems. Furthermore, it will potentially help pharmaceutical companies significantly decrease the huge cost of clinical trials and thus accelerate new drug discoveries.
Students, please do one or more of the following tests before contacting the mentors above.
Easy: Based on [1], implement an optimal adaptive trial design using any existing LP solver using R. Test it on a small size problem. Medium: Add some new Bayes constraints and increase the problem size. Hard: Since the core code should be implemented in C/C++. Write a simple package implementing Matrix multiplication. The main code should use C/C++. Mentors
- Ethan Fang, Assistant Professor, Penn State University, [email protected]
- Tuo Zhao, Assistant Professor, Georgia Tech, [email protected]
[1] Rosenblum M, Fang E, Liu H. Optimal, two-stage, adaptive enrichment designs for randomized trials using sparse linear programming, 2017.
[2] Mehrotra S. On the implementation of a primal-dual interior point method. SIAM Journal on optimization, 1992, 2(4): 575-601.